TY - JOUR

T1 - A stochastic model for cell sorting and measuring cell-cell adhesion

AU - Mochizuki, Atsushi

AU - Iwasa, Yoh

AU - Takeda, Yasuhiko

N1 - Funding Information:
This work was supported in part by a Grant!in!Aid for Scienti_c Research by the Ministry of Education\ Science\ and Culture\ Japan[ We thank the following people for their very useful comments] A[ Amagai\ H[ Doi\ H[ Ezoe\ K[ Fuchizaki\ J[ A[ Glazier\ Yoshito Harada\ Yuko Harada\ Y[ Haraguchi\ H[ Honda\ H[ Ide\ O[ Inomoto\ Y[ Iwai\ H[ Kagawa\ H[ Kawashima\ T[ Kubo\ Hirotsugu Matsuda\ Hiroyuki Matsuda\ T[ Murata\ K[ Nomura\ T[ Odagaki\ T[ Oyama\ A[ Sasaki\ K[ Sato\ M[ Sato!Maeda\ Y[ Sawada\ T[ Shiga\ N[ Shigesada\ Y[ Terada\ T[ Umeda\ N[ Wada and K[ Yamana[

PY - 1996/3/14

Y1 - 1996/3/14

N2 - Spontaneous sorting-out of cells of different types is studied by a lattice-structured model of continuous-time Markovian transition. Cells of two types, called black and white, are arranged on a regular lattice, and the adhesion between cells in contact depends on their types. Cells exchange their location with neighbors at random times, and the rate is affected by the difference in cell-to-cell adhesion caused by the exchange. The model has the unique equilibrium probability distribution of spatial patterns. According to the analysis equivalent to statistical thermodynamics, the spatial pattern should show a clear course grained segregation if the ratio of differential adhesion to the intensity of random movement (A/m) exceeds a critical value. However, even for the parameter range in which spatial pattern is predicted to be uniform, the cells of the same type tend to be in contact more often than in a random distribution, forming many small clusters of the same cell types. To quantify this microscopic tendency of aggregation, two statistics are introduced: (1) the fraction of black cells in the neighbor of a randomly chosen black cell (q(B/B)), and (2) the number of isolated black cells (IBC). The equilibrium value of these statistics can be predicted accurately using a pair-approximation method. However, if A/m is large, the convergence of q(B/B) to the equilibrium value takes an extremely long time. IBC is faster in convergence than q(B/B). These statistics can be used to measure the strength of differential adhesion relative to random movement (A/m) based on an observed spatial pattern of cells.

AB - Spontaneous sorting-out of cells of different types is studied by a lattice-structured model of continuous-time Markovian transition. Cells of two types, called black and white, are arranged on a regular lattice, and the adhesion between cells in contact depends on their types. Cells exchange their location with neighbors at random times, and the rate is affected by the difference in cell-to-cell adhesion caused by the exchange. The model has the unique equilibrium probability distribution of spatial patterns. According to the analysis equivalent to statistical thermodynamics, the spatial pattern should show a clear course grained segregation if the ratio of differential adhesion to the intensity of random movement (A/m) exceeds a critical value. However, even for the parameter range in which spatial pattern is predicted to be uniform, the cells of the same type tend to be in contact more often than in a random distribution, forming many small clusters of the same cell types. To quantify this microscopic tendency of aggregation, two statistics are introduced: (1) the fraction of black cells in the neighbor of a randomly chosen black cell (q(B/B)), and (2) the number of isolated black cells (IBC). The equilibrium value of these statistics can be predicted accurately using a pair-approximation method. However, if A/m is large, the convergence of q(B/B) to the equilibrium value takes an extremely long time. IBC is faster in convergence than q(B/B). These statistics can be used to measure the strength of differential adhesion relative to random movement (A/m) based on an observed spatial pattern of cells.

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U2 - 10.1006/jtbi.1996.0054

DO - 10.1006/jtbi.1996.0054

M3 - Article

AN - SCOPUS:0029996465

SN - 0022-5193

VL - 179

SP - 129

EP - 146

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

IS - 2

ER -